A cryptic rebus is a rebus that has the form of a cryptic clue. That is to say, there are two parts to a cryptic rebus:

a definition of the answer

a subsidiary indicator of the answer.

A definition can take the form of a picture which straightforwardly represents the answer, or it can be a synonym of the answer.

The subsidiary indicator of the answer, on the other hand, will be some kind of rebus word/image play which leads to the answer.

Here is an example:

This clue depicts a pen beside a sill, both above the word draw. The pen and sill are a rebus for PENCIL, which, when taken as a verb, is a synonym of draw. The word draw constitutes the definition of the clue, and the PEN + SILL rebus constitutes the subsidiary indicator.

This simple example illustrates the structure of a cryptic rebus.

Just like with purely verbal cryptic clues, however, it will not always be clear what constitutes the definition and what constitutes the subsidiary indicator. The definition of a cryptic rebus can appear anywhere (even misleadingly integrated in or around the subsidiary indicator). Part of the fun of these puzzles is the thrill the solver gets upon discovering where exactly to “split” the clue into its components.

Also like purely verbal cryptic clues, there is an exception to the rule that all clues consist of a definition and a subsidiary indicator. So-called double (or triple) rebuses comprise multiple rebuses, all of which, when solved, unequivocally signal the answer.

Lastly, rebuses can utilize any standard cryptic conventions. They can signal containment, reversals, beheadings, anagrams, and homophones. They can also make use of abbreviations.

Answers should indicate the solution, the definition, and the path to the solution. An answer to the above example would look something like:

PENCIL ([def] draw; PEN + SILL)

Now that you’re all caught up, let’s visit the museum. Please do not destroy the art in frustration:

*I don't own any of the images from which I drew in making these puzzles. Where possible I tried to use public domain images. I believe I may be using the rest in accordance with fair use.

$\begingroup$I would have thought the answer I came up with for #11 was just as obscure, but has been confirmed as being correct.$\endgroup$
– YowE3KJan 5 '17 at 6:50

$\begingroup$I'm with Neil: I think the step towards Append IX is good, but we are probably looking for something that comes before the appendix - be it in a book or in the digiestive system.$\endgroup$
– M OehmJan 5 '17 at 6:51